On the embedding of subalgebras corresponding to quotient actions in group-measure factors (Q1822018)

If X and Y are ergodic G spaces, where G is a countable discrete group and X is an extension of Y, we study the embedding of the group-measure von Neumann algebra corresponding to (Y,G) into the group-measure von Neumann algebra corresponding to (X,G). Necessary and sufficient conditions for the existence of a normal faithful conditional expectation are established. Under appropriate conditions the normalizer of the subalgebra is determined, and a correspondence between intermediate quotient actions and intermediate von Neumann algebras is established. A relationship between normal extensions with relatively discrete spectrum and crossed dual products of von Neumann algebras by compact second countable groups is determined.